The existence of a path-factor without small odd paths

2015/03/30 by Yoshimi Egawa, Egawa, Yoshimi, Michitaka Furuya +1 · 1 citation
Computer Science · Mathematics · #05C70 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO #msc:05C70

paper · pdf · doi:10.48550/arxiv.1503.08556

23 pages, 5 figures

arxiv created 2015/03/30 · openalex publication_date 2015/03/30 · arxiv updated 2015/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that if a graph G satisfies c₁(G-X)+(2)/(3)c₃(G-X)≤ (4)/(3)|X|+(1)/(3) for all X⊆ V(G), then G has a \P₂,P₅\-factor, where c_i(G-X) is the number of components C of G-X with |V(C)|=i.

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